.TH "hptrs" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
hptrs \- {hp,sp}trs: triangular solve using factor
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBchptrs\fP (uplo, n, nrhs, ap, ipiv, b, ldb, info)"
.br
.RI "\fBCHPTRS\fP "
.ti -1c
.RI "subroutine \fBcsptrs\fP (uplo, n, nrhs, ap, ipiv, b, ldb, info)"
.br
.RI "\fBCSPTRS\fP "
.ti -1c
.RI "subroutine \fBdsptrs\fP (uplo, n, nrhs, ap, ipiv, b, ldb, info)"
.br
.RI "\fBDSPTRS\fP "
.ti -1c
.RI "subroutine \fBssptrs\fP (uplo, n, nrhs, ap, ipiv, b, ldb, info)"
.br
.RI "\fBSSPTRS\fP "
.ti -1c
.RI "subroutine \fBzhptrs\fP (uplo, n, nrhs, ap, ipiv, b, ldb, info)"
.br
.RI "\fBZHPTRS\fP "
.ti -1c
.RI "subroutine \fBzsptrs\fP (uplo, n, nrhs, ap, ipiv, b, ldb, info)"
.br
.RI "\fBZSPTRS\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine chptrs (character uplo, integer n, integer nrhs, complex, dimension( * ) ap, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, integer info)"

.PP
\fBCHPTRS\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> CHPTRS solves a system of linear equations A*X = B with a complex
!> Hermitian matrix A stored in packed format using the factorization
!> A = U*D*U**H or A = L*D*L**H computed by CHPTRF\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix\&.
!>          = 'U':  Upper triangular, form is A = U*D*U**H;
!>          = 'L':  Lower triangular, form is A = L*D*L**H\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fINRHS\fP 
.PP
.nf
!>          NRHS is INTEGER
!>          The number of right hand sides, i\&.e\&., the number of columns
!>          of the matrix B\&.  NRHS >= 0\&.
!> 
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
!>          AP is COMPLEX array, dimension (N*(N+1)/2)
!>          The block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by CHPTRF, stored as a
!>          packed triangular matrix\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by CHPTRF\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is COMPLEX array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B\&.
!>          On exit, the solution matrix X\&.
!> 
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          The leading dimension of the array B\&.  LDB >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB114\fP of file \fBchptrs\&.f\fP\&.
.SS "subroutine csptrs (character uplo, integer n, integer nrhs, complex, dimension( * ) ap, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, integer info)"

.PP
\fBCSPTRS\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> CSPTRS solves a system of linear equations A*X = B with a complex
!> symmetric matrix A stored in packed format using the factorization
!> A = U*D*U**T or A = L*D*L**T computed by CSPTRF\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix\&.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fINRHS\fP 
.PP
.nf
!>          NRHS is INTEGER
!>          The number of right hand sides, i\&.e\&., the number of columns
!>          of the matrix B\&.  NRHS >= 0\&.
!> 
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
!>          AP is COMPLEX array, dimension (N*(N+1)/2)
!>          The block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by CSPTRF, stored as a
!>          packed triangular matrix\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by CSPTRF\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is COMPLEX array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B\&.
!>          On exit, the solution matrix X\&.
!> 
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          The leading dimension of the array B\&.  LDB >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB114\fP of file \fBcsptrs\&.f\fP\&.
.SS "subroutine dsptrs (character uplo, integer n, integer nrhs, double precision, dimension( * ) ap, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb, integer info)"

.PP
\fBDSPTRS\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> DSPTRS solves a system of linear equations A*X = B with a real
!> symmetric matrix A stored in packed format using the factorization
!> A = U*D*U**T or A = L*D*L**T computed by DSPTRF\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix\&.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fINRHS\fP 
.PP
.nf
!>          NRHS is INTEGER
!>          The number of right hand sides, i\&.e\&., the number of columns
!>          of the matrix B\&.  NRHS >= 0\&.
!> 
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
!>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
!>          The block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by DSPTRF, stored as a
!>          packed triangular matrix\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by DSPTRF\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B\&.
!>          On exit, the solution matrix X\&.
!> 
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          The leading dimension of the array B\&.  LDB >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB114\fP of file \fBdsptrs\&.f\fP\&.
.SS "subroutine ssptrs (character uplo, integer n, integer nrhs, real, dimension( * ) ap, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, integer info)"

.PP
\fBSSPTRS\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> SSPTRS solves a system of linear equations A*X = B with a real
!> symmetric matrix A stored in packed format using the factorization
!> A = U*D*U**T or A = L*D*L**T computed by SSPTRF\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix\&.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fINRHS\fP 
.PP
.nf
!>          NRHS is INTEGER
!>          The number of right hand sides, i\&.e\&., the number of columns
!>          of the matrix B\&.  NRHS >= 0\&.
!> 
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
!>          AP is REAL array, dimension (N*(N+1)/2)
!>          The block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by SSPTRF, stored as a
!>          packed triangular matrix\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by SSPTRF\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is REAL array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B\&.
!>          On exit, the solution matrix X\&.
!> 
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          The leading dimension of the array B\&.  LDB >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB114\fP of file \fBssptrs\&.f\fP\&.
.SS "subroutine zhptrs (character uplo, integer n, integer nrhs, complex*16, dimension( * ) ap, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, integer info)"

.PP
\fBZHPTRS\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> ZHPTRS solves a system of linear equations A*X = B with a complex
!> Hermitian matrix A stored in packed format using the factorization
!> A = U*D*U**H or A = L*D*L**H computed by ZHPTRF\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix\&.
!>          = 'U':  Upper triangular, form is A = U*D*U**H;
!>          = 'L':  Lower triangular, form is A = L*D*L**H\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fINRHS\fP 
.PP
.nf
!>          NRHS is INTEGER
!>          The number of right hand sides, i\&.e\&., the number of columns
!>          of the matrix B\&.  NRHS >= 0\&.
!> 
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
!>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
!>          The block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by ZHPTRF, stored as a
!>          packed triangular matrix\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by ZHPTRF\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B\&.
!>          On exit, the solution matrix X\&.
!> 
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          The leading dimension of the array B\&.  LDB >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB114\fP of file \fBzhptrs\&.f\fP\&.
.SS "subroutine zsptrs (character uplo, integer n, integer nrhs, complex*16, dimension( * ) ap, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, integer info)"

.PP
\fBZSPTRS\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> ZSPTRS solves a system of linear equations A*X = B with a complex
!> symmetric matrix A stored in packed format using the factorization
!> A = U*D*U**T or A = L*D*L**T computed by ZSPTRF\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix\&.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fINRHS\fP 
.PP
.nf
!>          NRHS is INTEGER
!>          The number of right hand sides, i\&.e\&., the number of columns
!>          of the matrix B\&.  NRHS >= 0\&.
!> 
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
!>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
!>          The block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by ZSPTRF, stored as a
!>          packed triangular matrix\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by ZSPTRF\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B\&.
!>          On exit, the solution matrix X\&.
!> 
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          The leading dimension of the array B\&.  LDB >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB114\fP of file \fBzsptrs\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.